Vsync or Vertical synchronization is a setting that matches your cards frame rate with your montors refresh rate.
If your video card is producing more FPS than your monitors refresh rate,typically 60hz or 60 times a second, you will get Tearing.
Or part of one frame and part of another frame displayed on the screen.
Examples.
https://www.google.com/search?q=screen+tearing&rls=com.microsoft:en-US:IE-Address&tbm=isch&tbo=u&source=univ&sa=X&ei=1vLcU6KDI5afyAT5vIC4Bw&ved=0CCsQsAQ&biw=1280&bih=879